Large Numbers & Operations — Class 5 IMO

7- and 8-digit Numbers & Place Value

After Lakhs come Ten Lakhs and Crores. One crore is written 1,00,00,000 (a 1 with seven zeros). The smallest 8-digit number is 1,00,00,000 and the largest is 9,99,99,999.

In 5,23,45,678 the 5 is in the Crores place and stands for 5,00,00,000. Each place is ten times the one to its right.

Example 1: What is the place value of 5 in 5,23,45,678?

5 is in the Crores place, so its value is 5,00,00,000.

Example 2: Write the smallest 8-digit number.

1,00,00,000 (one crore).

Quick recap

Places: Ones … Lakhs, Ten Lakhs, Crores.
1 crore = 1,00,00,000; smallest 8-digit number = 1 crore.

✓ Quick check

What is the place value of 4 in 3,45,67,890?

4 is in the Ten Lakhs place, so its value is 40,00,000.

1 crore equals how many lakhs?

1 crore = 100 lakhs.

Roman Numerals

Roman numerals use letters: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1000. A letter can be repeated up to three times to add (XXX = 30).

When a smaller letter comes before a larger one, we subtract: IV = 4, IX = 9, XL = 40, XC = 90, CD = 400, CM = 900.

Example 1: Write 24 in Roman numerals.

20 + 4 = XX + IV = XXIV.

Example 2: What number is CL?

C + L = 100 + 50 = 150.

Quick recap

I=1, V=5, X=10, L=50, C=100, D=500, M=1000.
Smaller before larger means subtract (IV=4, IX=9, XL=40).

✓ Quick check

Write 9 in Roman numerals.

9 is one less than 10, written IX.

What number is XL?

X before L means 50 − 10 = 40.

Operations & Estimation

Large numbers are added, subtracted, multiplied and divided just like smaller ones, place by place.

Estimation gives a quick, close answer. To estimate, round each number to the nearest lakh or crore first. So 4,56,789 rounded to the nearest lakh is 5,00,000.

Example 1: Round 4,56,789 to the nearest lakh.

The ten-thousands digit 5 is 5 or more, so it rounds up to 5,00,000.

Example 2: Add 12,34,567 + 23,45,433.

12,34,567 + 23,45,433 = 35,80,000.

Quick recap

Operate on large numbers place by place.
Estimate by rounding to the nearest lakh or crore.

✓ Quick check

Round 7,82,000 to the nearest lakh.

The ten-thousands digit 8 is 5 or more, so it rounds up to 8,00,000.

Subtract: 5,00,000 − 2,35,000 = ?

5,00,000 − 2,35,000 = 2,65,000.